Math / Numbers & Operations

Question $3 \frac{3}{8} \div 2 \frac{1}{4}=$

Studdy Solution

STEP 1

What is this asking? We're asked to divide two mixed numbers, which means figuring out how many times one "fits" into the other. Watch out! Don't forget to convert the mixed numbers to improper fractions before dividing!

STEP 2

1. Convert to Improper Fractions
2. Divide the Fractions
3. Simplify the Result

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions!
Remember, a mixed number is just a whole number plus a fraction hanging out together.
We've got $3 \frac{3}{8}$ and $2 \frac{1}{4}$ .

STEP 4

For $3 \frac{3}{8}$ , we multiply the whole number ( $3$ ) by the denominator ( $8$ ), which gives us $3 \cdot 8 = 24$ .
Then, we add the numerator ( $3$ ) to this result: $24 + 3 = 27$ .
This new number becomes our new numerator, and we keep the same denominator ( $8$ ).
So, $3 \frac{3}{8}$ becomes $\frac{27}{8}$ .

STEP 5

Now, let's do the same for $2 \frac{1}{4}$ .
Multiply the whole number ( $2$ ) by the denominator ( $4$ ): $2 \cdot 4 = 8$ .
Add the numerator ( $1$ ): $8 + 1 = 9$ .
Keep the same denominator ( $4$ ).
So, $2 \frac{1}{4}$ becomes $\frac{9}{4}$ .

STEP 6

Now, we're dividing $\frac{27}{8}$ by $\frac{9}{4}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{9}{4}$ is $\frac{4}{9}$ (just flip it!).

STEP 7

So, our division problem becomes: $\frac{27}{8} \div \frac{9}{4} = \frac{27}{8} \cdot \frac{4}{9}$ .

STEP 8

Let’s multiply those fractions!
Multiply the numerators together: $27 \cdot 4 = 108$ .
Multiply the denominators together: $8 \cdot 9 = 72$ .
So, we have $\frac{108}{72}$ .

STEP 9

We can simplify $\frac{108}{72}$ by finding the greatest common divisor (GCD) of $108$ and $72$ .
Turns out, their GCD is $36$ .

STEP 10

Now, we divide both the numerator and the denominator by $36$ : $\frac{108}{36} = 3$ and $\frac{72}{36} = 2$ .
This gives us the simplified fraction $\frac{3}{2}$ .

STEP 11

We can write $\frac{3}{2}$ as a mixed number. $2$ goes into $3$ one time with a remainder of $1$ .
So, $\frac{3}{2}$ is the same as $1 \frac{1}{2}$ .

STEP 12

Our final answer is $1 \frac{1}{2}$ .

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Question $3 \frac{3}{8} \div 2 \frac{1}{4}=$

Studdy Solution

STEP 1

What is this asking? We're asked to divide two mixed numbers, which means figuring out how many times one "fits" into the other. Watch out! Don't forget to convert the mixed numbers to improper fractions before dividing!

STEP 2

1. Convert to Improper Fractions
2. Divide the Fractions
3. Simplify the Result

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions!
Remember, a mixed number is just a whole number plus a fraction hanging out together.
We've got $3 \frac{3}{8}$ and $2 \frac{1}{4}$ .

STEP 4

STEP 5

Now, let's do the same for $2 \frac{1}{4}$ .
Multiply the whole number ( $2$ ) by the denominator ( $4$ ): $2 \cdot 4 = 8$ .
Add the numerator ( $1$ ): $8 + 1 = 9$ .
Keep the same denominator ( $4$ ).
So, $2 \frac{1}{4}$ becomes $\frac{9}{4}$ .

STEP 6

Now, we're dividing $\frac{27}{8}$ by $\frac{9}{4}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{9}{4}$ is $\frac{4}{9}$ (just flip it!).

STEP 7

So, our division problem becomes: $\frac{27}{8} \div \frac{9}{4} = \frac{27}{8} \cdot \frac{4}{9}$ .

STEP 8

Let’s multiply those fractions!
Multiply the numerators together: $27 \cdot 4 = 108$ .
Multiply the denominators together: $8 \cdot 9 = 72$ .
So, we have $\frac{108}{72}$ .

STEP 9

We can simplify $\frac{108}{72}$ by finding the greatest common divisor (GCD) of $108$ and $72$ .
Turns out, their GCD is $36$ .

STEP 10

Now, we divide both the numerator and the denominator by $36$ : $\frac{108}{36} = 3$ and $\frac{72}{36} = 2$ .
This gives us the simplified fraction $\frac{3}{2}$ .

STEP 11

We can write $\frac{3}{2}$ as a mixed number. $2$ goes into $3$ one time with a remainder of $1$ .
So, $\frac{3}{2}$ is the same as $1 \frac{1}{2}$ .

STEP 12

Our final answer is $1 \frac{1}{2}$ .

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Question338÷214=3 \frac{3}{8} \div 2 \frac{1}{4}=383​÷241​=

Studdy Solution

STEP 1

What is this asking? We're asked to divide two mixed numbers, which means figuring out how many times one "fits" into the other. Watch out! Don't forget to convert the mixed numbers to improper fractions before dividing!

STEP 2

1. Convert to Improper Fractions2. Divide the Fractions3. Simplify the Result

STEP 3

Alright, let's **kick things off** by turning these mixed numbers into improper fractions!Remember, a mixed number is just a whole number plus a fraction hanging out together.We've got 3383 \frac{3}{8}383​ and 2142 \frac{1}{4}241​.

STEP 4

STEP 5

Now, let's do the same for 2142 \frac{1}{4}241​.Multiply the whole number (222) by the denominator (444): 2⋅4=82 \cdot 4 = 82⋅4=8.Add the numerator (111): 8+1=98 + 1 = 98+1=9.Keep the same denominator (444).So, 2142 \frac{1}{4}241​ becomes 94\frac{9}{4}49​.

STEP 6

Now, we're dividing 278\frac{27}{8}827​ by 94\frac{9}{4}49​.Remember, dividing by a fraction is the same as multiplying by its reciprocal.The reciprocal of 94\frac{9}{4}49​ is 49\frac{4}{9}94​ (just flip it!).

STEP 7

So, our division problem becomes: 278÷94=278⋅49\frac{27}{8} \div \frac{9}{4} = \frac{27}{8} \cdot \frac{4}{9}827​÷49​=827​⋅94​.

STEP 8

Let’s multiply those fractions!Multiply the numerators together: 27⋅4=10827 \cdot 4 = 10827⋅4=108.Multiply the denominators together: 8⋅9=728 \cdot 9 = 728⋅9=72.So, we have 10872\frac{108}{72}72108​.

STEP 9

We can simplify 10872\frac{108}{72}72108​ by finding the **greatest common divisor** (GCD) of 108108108 and 727272.Turns out, their GCD is 363636.

STEP 10

Now, we divide both the numerator and the denominator by 363636: 10836=3\frac{108}{36} = 336108​=3 and 7236=2\frac{72}{36} = 23672​=2.This gives us the **simplified fraction** 32\frac{3}{2}23​.

STEP 11

We can write 32\frac{3}{2}23​ as a mixed number. 222 goes into 333 one time with a remainder of 111.So, 32\frac{3}{2}23​ is the same as 1121 \frac{1}{2}121​.

STEP 12

Our **final answer** is 1121 \frac{1}{2}121​.

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Question $3 \frac{3}{8} \div 2 \frac{1}{4}=$

1. Convert to Improper Fractions
2. Divide the Fractions
3. Simplify the Result

Alright, let's kick things off by turning these mixed numbers into improper fractions!
Remember, a mixed number is just a whole number plus a fraction hanging out together.
We've got $3 \frac{3}{8}$ and $2 \frac{1}{4}$ .

Now, let's do the same for $2 \frac{1}{4}$ .
Multiply the whole number ( $2$ ) by the denominator ( $4$ ): $2 \cdot 4 = 8$ .
Add the numerator ( $1$ ): $8 + 1 = 9$ .
Keep the same denominator ( $4$ ).
So, $2 \frac{1}{4}$ becomes $\frac{9}{4}$ .

Now, we're dividing $\frac{27}{8}$ by $\frac{9}{4}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{9}{4}$ is $\frac{4}{9}$ (just flip it!).

So, our division problem becomes: $\frac{27}{8} \div \frac{9}{4} = \frac{27}{8} \cdot \frac{4}{9}$ .

Let’s multiply those fractions!
Multiply the numerators together: $27 \cdot 4 = 108$ .
Multiply the denominators together: $8 \cdot 9 = 72$ .
So, we have $\frac{108}{72}$ .

We can simplify $\frac{108}{72}$ by finding the greatest common divisor (GCD) of $108$ and $72$ .
Turns out, their GCD is $36$ .

Now, we divide both the numerator and the denominator by $36$ : $\frac{108}{36} = 3$ and $\frac{72}{36} = 2$ .
This gives us the simplified fraction $\frac{3}{2}$ .

We can write $\frac{3}{2}$ as a mixed number. $2$ goes into $3$ one time with a remainder of $1$ .
So, $\frac{3}{2}$ is the same as $1 \frac{1}{2}$ .

Our final answer is $1 \frac{1}{2}$ .